Lesson Worksheet: Equation of a Straight Line: Vector Form Mathematics

In this worksheet, we will practice finding the equation of a straight line in vector form.

Q1:

Which of the following can be the vector form of the equation of the straight line 𝑎𝑥+𝑏𝑦+𝑐=0, where 𝑎0 and 𝑏0?

  • Ar=𝑐𝑎,0+𝐾𝑎,𝑏
  • Br=0,𝑐𝑏+𝐾𝑏,𝑎
  • Cr=0,𝑐𝑏+𝐾𝑏,𝑎
  • Dr=𝑐𝑎,0+𝐾𝑎,𝑏
  • Er=𝑐𝑎,0+𝐾𝑎,𝑏

Q2:

Which of the following can be the vector form of the equation of the straight line 𝑥𝑎+𝑦𝑏=1, where 𝑎0 and 𝑏0?

  • Ar=𝑎,0+𝐾𝑎,𝑏
  • Br=0,1𝑎+𝐾(𝑏,𝑎)
  • Cr=0,𝑏+𝐾𝑎,𝑏
  • Dr=0,1𝑏+𝐾𝑏,𝑎
  • Er=1𝑎,0+𝐾𝑏,𝑎

Q3:

Find the vector equation of the straight line passing through the origin and the point (0,4).

  • Ar=0,4
  • BrK=4,0
  • Cr=4,0
  • DrK=0,4

Q4:

Find the vector equation of the straight line passing through the points (6,7) and (4,6).

  • Ar=4,6+𝐾13,10
  • Br=4,6+𝐾10,13
  • Cr=6,7+𝐾10,13
  • Dr=6,4+𝐾7,6

Q5:

Find the vector equation of the straight line whose slope is 83 and passes through the point (4,9).

  • Ar=3,8+𝐾4,9
  • Br=4,9+𝐾8,3
  • Cr=9,4+𝐾3,8
  • Dr=4,9+𝐾3,8

Q6:

Consider the line through the point (3,6) and perpendicular to vector r=3,6. Which of the following is a vector equation of this line?

  • A𝐾=3,6+6,3r
  • Br=3,6+𝐾6,3
  • Cr=3,6+𝐾3,6
  • Dr=6,3+𝐾3,6
  • E𝐾=3,6+3,6r

Q7:

Write the vector equation of the straight line that passes through the point (6,9) with direction vector 9,2.

  • Ar=9,2+𝑘6,9
  • Br=6,9+𝑘9,2
  • Cr=9,2+𝑘6,9
  • Dr=6,9+𝑘9,2

Q8:

Find the vector equation of the straight line that is parallel to the 𝑥-axis and passing through the point (5,2).

  • ArK=2,5+1,0
  • BrK=5,2+1,0
  • CrK=2,5+0,1
  • DrK=5,2+0,1

Q9:

Given that 9,1 and 8,𝑚 are the direction vectors of two perpendicular straight lines, determine the value of 𝑚.

  • A72
  • B72
  • C89
  • D89

Q10:

Suppose that a line has direction vector u=21,4. What, to the nearest second, is the measure of the positive angle that this line makes with the positive 𝑥-axis?

  • A1691257
  • B791257
  • C100473
  • D10473

This lesson includes 22 additional questions and 216 additional question variations for subscribers.

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